Hitherto, various electronic watermark schemes have been proposed and been developed. It is difficult to remove an electronic watermark from an image unless the key information for extracting it is available. Therefore, it is being widely used for the purpose of copyright protection, such as the prevention of tampering and illegal copy of images.
For example, Non-Patent Document 1 proposes an electronic watermark method using singular value decomposition (SVD).
More specifically, in order to embed an electronic watermark, singular value decomposition is performed on an original image A to acquire a singular value S and singular vectors U and V. Next, an electronic watermark W is embedded to the singular value S to create (S+αW). This further undergoes singular value decomposition to acquire a singular value Sw and singular vectors Uw and Vw. Then, the singular value Sw is multiplied by the singular vectors U and VT, which are acquired by the first singular value decomposition, from both sides to create an electronic-watermark-embedded image Aw(=USwVT).
In order to detect an electronic watermark, singular value decomposition is performed on an examination target image Aw* to acquire the singular value Sw*. Next, the singular value Sw* is calculated by the singular vectors Uw* and Vw*T from both sides to calculate D*(=Uw*Sw*Vw*T). Then, W*=(D*−S)/α acquired by performing expression transformation on D*=(S+αW*) is used to detect an electronic watermark W*.
[Non-Patent Document 1] Ruizhen Liu et al, “An SVD-Based Watermarking Scheme for Protecting Rightful Ownership”, IEEE Transactions on Multimedia, March in 2002, Vol. 4, No. 1, pp. 121-128
[Non-Patent Document 2] Xiao-Ping Zhang, “Comments on “An SVD-Based Watermarking Scheme for Protecting Rightful Ownership”, IEEE Transactions on Multimedia, April in 2005, Vol. 7, No. 2, pp. 593-594